In this notebook we will develop code to estimate the number of
collected photons from a single fluorophore for a given exposure time.
To do this we will need to find the following parameters for our given
experiment:

Here we will estimate the photon flux on the fluorophore. It is
important to note that the absorption cross-section is a strong function
of wavelength and that whatever illumination source is also strongly
wavelength dependent. Do we will have to make several assumptions:

Illumination power is not a strong function of wavelength.

Absorbtion is also relatively constant.

Alright, lets start with some code.

importnumpyasnpimportpylabaspltfrommathimportlog,asin,pi,cos

Now lets calculate the photon flux at the sample.

For now, we are going to use the order of magnitude approximation from
this
pdf.

This source gives that the photon flux is about
\(3.6 x 10^{20} \frac{photons}{cm^2}\)

# To Do: Need to make this more explicit. Probably several code blocks corresponding to broadband and led.power_out=.22# Watts, conservative estimate of total output of Spectra X in infrared.illumination_area=12.0e-6# cm^2 This is a function of the viewing area and Numerical aperture of objective.illumination_flux=power_out/illumination_areawavelength=380.0e-9# metersh=6.626e-34# Jouls/sc=2.998e8# m/sphoton_flux=illumination_flux*wavelength/h/c#photon_flux = 3.6e20 # photons / cm^2print(photon_flux,'Photon Flux')

percent_collected*=0.85# Dichroic Mirrorpercent_collected*=0.80# Long pass filterpercent_collected*=0.98**5# Assume several surfaces, but that they have antireflective coating.print(percent_collected,'%')

(0.18764585734425032,'%')

Great, now we just need to multiply this by the emitted photons and we
have our photon rate.

How does this affect image quality? Well, now that we know how many
photons are reaching the camera we can start looking at how many are
recorded per frame. This is affected, largely, by two parameters:

Exposure Time

Quantum Efficiency

Exposure time is fairly straight forward, how long a time does each
pixel collect light. Quantum efficiency is the percentage chance that
each photon will actually be recorded.